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H = distance from the axis of rotation to the center of mass Theoretical Derivation of the Period of a Physical Pendulum Period of a Physical Pendulum.

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Presentation on theme: "H = distance from the axis of rotation to the center of mass Theoretical Derivation of the Period of a Physical Pendulum Period of a Physical Pendulum."— Presentation transcript:

1 h = distance from the axis of rotation to the center of mass Theoretical Derivation of the Period of a Physical Pendulum Period of a Physical Pendulum

2 Theoretical Derivation of the Period of a Physical Pendulum Small Angle Approximation For small θ h = distance from the axis of rotation to the center of mass For small angles a physical pendulum acts like an angular simple harmonic oscillator since the torque is proportional to the opposite of the angular position.

3 h = distance from the axis of rotation to the center of mass Period of a Physical Pendulum Theoretical Derivation of the Period of a Physical Pendulum But Angular frequency of a physical pendulum

4 Period of a Physical Pendulum h = distance from the axis of rotation to the center of mass Period of a Physical Pendulum Theoretical Derivation of the Period of a Physical Pendulum But

5 Period of a Physical Pendulum What if the physical pendulum is a simple pendulum of mass m and length L ? But So a simple pendulum is just a physical pendulum where all of the mass is at a distance L from the axis of rotation.

6 But Period of a Physical Pendulum

7 Period Period of a Physical Pendulum


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